An important feature of these MMD norms, compared to OT distances (see Section REF ) is that they suffer less from the curse of dimensionality [1]}, [2]}. The intuition is that the discrete formula (REF ) is similar to a Monte-Carlo integration technique to approximate (REF ). If the \((x_i)_i\)  are drawn independently from \(\) , this explains why the discretization error is of the order \(1/\sqrt{N}\) , and the decay with \(N\)  is independent of the dimension.
